Statement 1: For a singular square matrix `A ,A B=A C B=Cdot` Statement 2; `|A|=0,t h e nA^(-1)` does not exist.

If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1))^(-1)| is ___________.

Statement 1: if a ,b ,c ,d are real numbers and A=[a b c d]a n dA^3=O ,t h e nA^2=Odot Statement 2: For matrix A=[a b c d] we have A^2=(a+d)A+(a d-b c)I=Odot

Which of the following statements is/are true about square matrix A or order n ? (-A)^(-1) is equal to A^(-1)w h e nn is odd only If A^n-O ,t h e nI+A+A^2++A^(n-1)=(I-A)^(-1)dot If A is skew-symmetric matrix of odd order, then its inverse does not exist. (A^T)^(-1)=(A^(-1))^T holds always.

Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i is a 2 xx 2 identity matrix, Tr(A) i= sum of diagonal elements of A and |A| = determinant of matrix A. Statement 1:Tr(A)=0 Statement 2: |A| =1 . then (A) Statement 1 is false, statement 2 is true. (B) Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1. (C) Statement 1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1. (D) Statement 1 is true, statement 2 is false.

Statement 1 : The area of the triangle formed by the points A(1000 ,1002),B(1001 ,1004),C(1002 ,1003) is the same as the area formed by the point A^(prime)(0,0),B^(prime)(1,2),C^(prime)(2,1) Statement 2 : The area of the triangle is constant with respect to the translation of axes. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: The number of positive integral solutions of a b c=30 is 27. Statement 2: Number of ways in which three prizes can be distributed among three persons is 3^3 (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: The inverse of singular matrix A=([a_(i j)])_(nxxn), \ w h e r e \ a_(i j)=0,igeqj \ i s \ B=([a i j^-1])_(nxxn) . Statement 2: The inverse of singular square matrix does not exist.

Statement 1: If differentiable function f(x) satisfies the relation f(x)+f(x-2)=0AAx in R , and if (d/(dx)f(x))_(x=a)=b ,t h e n(d/(dx)f(x))_(x=a+4000)=b . Statement 2: f(x) is a periodic function with period 4. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Consider a curve C : y^2-8x-2y-15=0 in which two tangents T_1a n dT_2 are drawn from P(-4,1) . Statement 1: T_1a n dT_2 are mutually perpendicular tangents. Statement 2: Point P lies on the axis of curve Cdot (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1: Line (x-1)/1=(y-0)/2=(z+2)/(-1) lies in the plane 2x-3y-4z-10=0. Statement 2: if line vec r= vec a+lambda vec b lies in the plane vec r. vec c=n (where n is scalar),then vec b. vec c=0. (a) Both the statements are true, and Statement 2 is the correct explanation for Statement 1. (b) Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1. (c)Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.